Hook size is the diameter of a crochet hook, which controls how big each stitch is. Sizes are given in millimeters and US letter/number labels (e.g. 5.0 mm = H-8). A larger hook makes bigger, looser stitches; a smaller hook makes tighter ones.
Patterns recommend a hook size, but the real goal is matching gauge — adjust up or down a size to hit it. For amigurumi, makers deliberately use a hook smaller than the yarn label suggests so the fabric stays tight enough to hide stuffing.